Sums of products of s-Fibonacci polynomial sequences

We consider s-Fibonacci polynomial sequences (F0 (x), Fs (x), F2s (x), . . .), where s ∈ N is given. By studying certain z-polynomials involving s-polyfibonomials n k Fs(x) = Fsn(x)···Fs(n−k+1)(x) Fs(x)···Fks(x) and s-Gibonacci polynomial sequences (G0 (x), Gs (x), G2s (x), . . .), we generalize some known results (and obtain some new results) concerning sums of products and addition formulas of Fibonacci numbers

We consider s-Fibonacci polynomial sequences (F0 (x), Fs (x), F2s (x), . . .), where s ∈ N is given. By studying certain z-polynomials involving s-polyfibonomials n k Fs(x) = Fsn(x)···Fs(n−k+1)(x) Fs(x)···Fks(x) and s-Gibonacci polynomial sequences (G0 (x), Gs (x), G2s (x), . . .), we generalize some known results (and obtain some new results) concerning sums of products and addition formulas of Fibonacci numbers